Well I live here and typically go to a game or 2 every year.

The teams may or may not practice at the stadium where they play. There are practice fields near the stadiums too, which may be used. I think it was in 2010 when I was out riding, I saw a team practicing on fields in Chandler, when there hasn't been a team there for about 10 years (the Brewers left in 1997).

If you want to see the players up close, my suggestion is to go to a game early, and/or buy seats close to the field. The teams will usually practice on the stadium field before the game, and they take time for photos, autographs, etc before the game starts.

You'd usually have more of a chance seeing a team at one of the not-so-busy stadiums and/or not-so-popular opponent. Nearly all of the Giants and Cubs home games in Scottsdale/Mesa sell out, but it may be a little easier to see them say in Maryvale. Avoiding Fri-Sat-Sun usually helps too. Actually, I rather like the Maryvale stadium, close enough to get to it and decent freeway access, prices aren't too horrible, and it just seems more down to earth. The downtown Scottsdale stadium can get crazy... I went to a game at Salt River Field this year, and it was good, but on the verge of being too popular.